A stochastic maximum principle for processes driven by fractional Brownian motion

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter H=(H1,…,Hm)∈(12,1)m. As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion.